Some Rambling on Order Theory and Logic

This is a followup to yesterday's rambling: Freya Holmér - Why Can't You Multiply Vectors?

See The Life and Letters of Lewis Carroll (just below the photograph of George Macdonald and his daughter Lilly):

In November he gave a lecture at a meeting of the Ashmolean Society on "Where does the Day begin?" The problem, which was one he was very fond of propounding, may be thus stated: If a man could travel round the world so fast that the sun would be always directly above his head, and if he were to start travelling at midday on Tuesday, then in twenty-four hours he would return to his original point of departure, and would find that the day was now called Wednesday—at what point of his journey would the day change its name? The difficulty of answering this apparently simple question has cast a gloom over many a pleasant party.

See Partially ordered group:

In abstract algebra, a partially ordered group is a group (G, +) equipped with a partial order "≤" that is translation-invariant; in other words, "≤" has the property that, for all a, b, and g in G, if a ≤ b then a + g ≤ b + g and g + a ≤ g + b.

It's not a Sugar Pine. I don't know where I got that idea from. California, probably.

On Euclid's use of Common Notions, see Guerilla Logic Page 7:

See Local hidden-variable theory for an idea of what a non-local hidden-variable theory isn't.

I checked and the rain started at 11:55 AM.

See Order isomorphism, Galois connection and Freya Holmér - Vectors and Dot Product (Math for Game Devs Part I). Or just skip to the rocket game if you're not interested in knowing anything about it!